Coupled Tensor Completion via Low-rank Tensor Ring

The coupled tensor decomposition aims to reveal the latent data structure which may share common factors. As a quantum inspired representation for tensors, the recently proposed tensor ring decomposition shows powerful representational ability. Using this decomposition, a novel non-convex model using the coupled tensor ring Frobenius norm is proposed in this paper. We also provide an excess risk bound for this model, which shows improvement compared with the recent coupled nuclear norm method. The model is solved by the block coordinate descent which only involves solving a series of quadratic forms constructed by the sampling pattern, thus it leads to efficient optimization. The proposed algorithm is validated on synthetic data and real-world data, which demonstrates the superiority over the existing coupled completion methods.